Whisk the flour, baking powder, baking soda, and salt in a medium bowl until the color is even. Toss the dried berries with 1 tablespoon of flour. Zest and juice the lemon.

Rub the zest into the sugar, then beat it with the softened butter on medium speed for 3 minutes, until pale yellow and fluffy like thick frosting.

Beat in the eggs one at a time, 30 seconds after each. Stir in the vanilla and lemon juice until the batter is smooth and glossy.

Add the flour mixture in three parts, alternating with the sour cream and milk, beginning and ending with flour. Mix on low until the last streak of flour disappears, then stop.

Spread 1 cup of the plain batter across the bottom of the pan. Fold the floured berries into the rest with 8 to 10 strokes, until a few purple streaks show, then spoon it over the plain layer.

Smooth the top and sprinkle with the turbinado sugar until the surface glitters.

Set the pan on a rimmed baking sheet and bake on the center rack at 350°F for 55 minutes, checking at 50. The top should be deep golden brown and spring back when pressed, with the center at 205°F to 210°F. If the sugar darkens past golden before 35 minutes, tent loosely with foil.

Cool in the pan on a wire rack for 20 minutes, then run a thin knife around the edge and release the ring. Cool 30 more minutes, until the sides feel barely warm, before slicing.